How do I bisect along an axis?
Bisect tool has the Plane Normal option in its settings. It consists of 3 sliders for each axis with values between -1 and 1 which allow to control the orientation of the cutting plane. 

The values below or above 0 will make the custom plane to be oriented towards that axis, while values of 0 or around mean that the plane will be oriented along that axis.

In your case enter 0 value for the Z axis: